Vagueness, Gunk, and Boundaries

Three residual questions about parts and wholes, each of which turns out to bear on the debates already surveyed. Can the world itself be indeterminate, or is all vagueness in our language? Must matter bottom out in simples, or could it divide without end? And what are the boundaries of things — surfaces, edges, the point where one object stops and the next begins?

Ontic and semantic vagueness

"Bald" is vague: there are men who are neither clearly bald nor clearly not. The standard diagnosis is semantic: the world contains a precise number of hairs, and the vagueness lies in our word, which fails to draw a sharp line. On this view vagueness is a feature of representation, and reality is perfectly determinate.

Ontic vagueness is the claim that the world itself can be indeterminate — that there are objects with genuinely fuzzy boundaries, or cases where it is a matter of fact that there is no fact. It matters here because the argument from vagueness against restricted composition assumes vagueness must be semantic, and ontic vagueness is the natural escape.

The main obstacle is Evans' argument that there cannot be vague identity. Suppose it is indeterminate whether $a = b$ . Then $b$ has the property being such that it is indeterminate whether $a$ is identical to it. But $a$ does not have that property, since it is determinate that $a = a$ . So $a$ and $b$ differ in a property, so by Leibniz's Law they are determinately distinct — contradicting the assumption.

The argument is short and its interpretation is contested. Objections include: whether "it is indeterminate whether $a = \cdot$ " expresses a genuine property; whether the contrapositive step is valid in a logic with truth-value gaps; and whether the argument shows only that vague identity statements are impossible while leaving vague objects untouched. What can be said is that ontic vagueness is not free — it requires either rejecting a step in a very short proof or accepting a non-classical logic, and the latter has costs throughout.

The mereological application is the problem of the many discussed under material constitution: the cat on the mat has millions of equally good candidate boundaries. Ontic vagueness would say the cat has a genuinely fuzzy boundary; semantic vagueness says "the cat" fails to determinately denote any one candidate; nihilism says there is no cat.

Gunk

Atomless gunk is matter every part of which has proper parts. There are no simples; division goes on without end. The notion is Lewis's coinage, and its interest is that it appears perfectly coherent — one can write down a model of classical mereology with no atoms — yet it contradicts positions that are otherwise attractive.

$\forall x \exists y (y ⊏ x)$

Its consequences:

Nihilism cannot be true if the world is gunky. Nihilism says only simples exist. If there are no simples and no composites, nothing exists, which is absurd. The nihilist must therefore hold that gunk is impossible — a strong modal claim about the structure of matter, defended a priori, which is uncomfortable.
The atomist's commitment is also empirical. Whether the world is gunky is not obviously an armchair question. Physics gives no clear verdict: the particle inventory of the Standard Model looks atomistic, but effective field theory presents a tower of descriptions with no evident floor, and the question of whether spacetime is continuous or discrete at the Planck scale is open.
Junk and hunk. The dual notion — junk, where every object is a proper part of some larger object, so there is no universe — threatens unrestricted composition, which requires a fusion of everything. Hunk is a world that is both gunky and junky.

The continuum questions here are the same ones Zeno raised, and they connect to the treatment of infinite divisibility in Zeno and the continuum and to the infinitesimal alternatives in non-standard analysis. What ontology adds is the question whether the structure of matter must mirror the structure of the mathematical continuum used to describe it — and the answer is not obviously yes, since the continuum may be a representational convenience rather than a claim about parts.

Boundaries and contact

Where exactly does an object end? The question is Brentano's, and it produces a genuine puzzle about how two things can touch.

Consider a solid sphere resting on a plane, or a block cut in two. Does the boundary belong to one side, the other, both, or neither?

If the boundary belongs to both, they share a part, and it is unclear that they are two objects rather than one.
If it belongs to neither, there is a gap of measure zero between them containing nothing, which is strange.
If it belongs to one — say the left half is closed and the right half open — then the two halves are asymmetric for no reason, and the right half has no outermost point.

Brentano's response was that boundaries are ontologically dependent entities: a surface cannot exist without the body it bounds, and two touching bodies can share a boundary because a boundary is not a further object with parts of its own. Modern treatments distinguish bona fide boundaries (physical discontinuities, like a coastline) from fiat ones (drawn by us, like a state border), which is a useful distinction and not obviously a metaphysical one.

The same problem in a temporal key concerns the instant of change: at the moment a light goes on, is it on or off? The options — the last instant of dark, the first of light, both, neither — mirror the spatial case exactly, which suggests the difficulty is about the topology of continua rather than about matter.

Location and multilocation

A final residual question. Mereology says how parts relate to wholes; it says nothing about how things relate to places. The relation needs its own theory, and the cases that force it are the ones already met:

An immanent universal is wholly present wherever it is instantiated — multilocation of the most extreme kind.
An endurantist object is wholly present at each moment of its career, which is multilocation in time.
Coincident objects such as Goliath and Lumpl occupy the same region without being identical.

A common framework distinguishes exact location (the region a thing exactly fills), weak location (any region it overlaps), and pervasive and entire location. Once these are separated, several of the disputes above turn out to be about which relation is meant, and some apparent impossibilities become merely unfamiliar.

Where these questions sit

These are category questions at the margin, but their significance is that they constrain the headline debates. Ontic vagueness, if available, saves the moderate answer to the Special Composition Question. Gunk, if possible, refutes nihilism outright. Boundaries and location determine whether coincidence is even statable. In each case a question that looks like a technicality turns out to be where a major position lives or dies — which is a general feature of ontology, and a reason for taking the formal apparatus seriously rather than treating it as bookkeeping.